When doping a semiconductor layer, such as when forming an n-well, an edge of a resist may scatter a portion of the dopant into exposed regions of the layer. Accordingly, dopant that impacts the edge of the resist may be deflected into the non-resist covered region. Such scattered dopant will typically be deposited a certain distance from the resist edge at a shallow depth relative to the unscattered dopant and is referred to as a scatter-doped region. Because the scatter-doped region lies at a shallow depth, the scattered dopanted region is positioned in a region apart from the main doped area and thus may alter the characteristics of a semiconductor device.
Because the scatter-doped area may alter the characteristics of a semiconductor device, it is advantageous to predict the location, depth and concentration of dopant in the scatter-doped region in order to better anticipate the semiconductor devices actual operating characteristics. Accordingly, once the characteristics of the scatter-doped region can be determined for a particular doping configuration, the effect of the scatter-doped region can be anticipated and the semiconductor design altered accordingly if necessary.
Scattering can occur from the edge of a resist during doping when doping particles strike scattering centers in the resist proximate to the edge of the resist. The doping particles may include either positive or negative ions, etc. Scattering centers of the resist typically include molecules which make up the resist. Accordingly, when the doping particles travel into the resist and strike a scattering center, the doping ion may be deflected by the scattering center. If the scattering center lies close to an edge of the resist, the scattered dopant particle may be deflected out of the resist into an adjacent region. The angle of deflection of the doping ions can be in virtually any direction from the scattering center; however, the doping ions will have a preferred range of scattering angles and generally will be distributed about a particular scattering angle with a Gaussian distribution.
In addition to having a scattering angle, doping ions will lose velocity when they are scattered by the scattering center, and the scattered velocity may be virtually any velocity lower than the original velocity of the scattered doping ion. However, there will be a statistically preferred scatter velocity with the other velocities generally distributed about the statistically preferred scatter velocity with a Gaussian distribution. Thus, the process of scattering doping ions off of scattering centers in an edge of a resist can be statistically known, and it becomes possible to determine the location of a scatter-doped region using various parameters such as doping ion type, doping ion velocity, resist type, resist edge location, etc. Consequently, it is advantageous to vary the location of a resist edge with increased flexibility.
In other words, it is known that the surface doping in n-FETs is affected by the proximity of nearby n-wells through ion scattering from mask edges, also known as the lateral straggle mechanism. There is also a complementary effect to p-FETs near n-FETs by ion scattering. Accordingly, to calculate an actual threshold voltage of such transistors, it is necessary to know how close a device is to nearby wells. Standard techniques for calculating such an effect typically involves shrinking and expanding n-well shapes to find FETs within a given distance from the n-well's edges. Device gates falling within this given distance are then intersected or overlapped with the expanded n-well shape and these intersected shapes are then bucketed based on distance from the n-well.
For example, for a U-shaped n-well, if the shape is expanded in all directions, the vertical components of the inside edges of the n-well will eventually merge at a point equidistant from both edges. If a FET gate exists within the U-shape, it will experience scattering effects from the n-well edges. While the typical shrink/expand method gave an estimate of a potential shift in threshold voltage, a more accurate method is desirable. Improved accuracy is needed because when multiple n-wells are close to the same gate, the typical shrink/expand technique often has difficulty accounting for a resulting increase in scattering.
Because the standard algorithms are shaped-based, U-shaped wells surrounding a device gate are considered an influence on the gate. Additionally, standard methods can intersect a merged shape with a gate to receive an area parameter that could be passed onto a simulation model. However, a merged or single shape approach does not take into account the fact that it is the n-well edges and not the n-well shape that defines scattering effects.